Subgroups — C₂×C₇×#3256 #13238122

Order 1792.

1930 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#529	C₂	1	2	yes	maximal, complemented
2	C₇×#3256	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₇×#479	C₂	1	2	yes	maximal, complemented
4	C₂×C₇×#478	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#470	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#469	C₂	1	1	yes	maximal, characteristic
7	C₂×C₇×#468	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#464	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#463	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#423	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
13	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
14	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
16	C₇×#529	—	2	8	no	—
17	C₇×#529	C₂²	1	16	yes	complemented
18	C₂×C₇×#126	—	2	2	no	—
19	C₂×C₇×#125	C₂²	1	2	yes	—
20	C₂×C₇×#124	C₂²	1	2	yes	—
21	C₂×C₇×#123	—	2	2	no	—
22	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₇×#121	C₂²	1	2	yes	—
24	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
25	C₂×C₄×C₇×D₄	—	2	2	no	—
26	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
27	C₂×C₇×#117	—	2	2	no	—
28	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
29	C₇×#479	C₂²	1	16	yes	complemented
30	C₇×#478	C₂²	1	16	yes	complemented
31	C₇×#470	C₂²	1	8	yes	complemented
32	C₇×#469	C₂²	1	8	yes	—
33	C₇×#468	C₂²	1	16	yes	complemented
34	C₇×#464	C₂²	1	16	yes	complemented
35	C₇×#463	C₂²	1	16	yes	complemented
36	C₂×C₇×#107	C₂²	1	2	yes	—
37	C₂×C₇×#106	C₂²	1	1	yes	characteristic
38	C₂×C₇×#106	C₂²	1	1	yes	characteristic
39	C₇×#423	C₂²	1	8	yes	complemented
40	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
41	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
42	C₂×C₇×#103	C₂²	1	2	yes	—
43	C₂×C₇×#103	C₂²	1	2	yes	—
44	C₂×C₇×#102	C₂²	1	2	yes	—
45	C₂×C₇×#102	C₂²	1	2	yes	—
46	C₂×#3256	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₂²×C₇×Q₈	C₂³	1	2	yes	—
48	C₂²×C₇×D₄	—	2	2	no	—
49	C₂²×C₇×D₄	C₂³	1	2	yes	—
50	C₂³×C₄×C₇	—	2	2	no	—
51	C₂³×C₄×C₇	D₄	1	2	yes	—
52	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
53	C₂×C₇×Q₁₆	—	4	2	no	—
54	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
55	C₂×C₇×SD₁₆	—	4	4	no	—
56	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
57	C₂×C₇×D₈	—	4	2	no	—
58	C₂×C₇×D₈	C₂³	1	4	yes	—
59	C₂×C₇×M₁₆	—	4	2	no	—
60	C₂×C₇×M₁₆	—	4	2	no	—
61	C₂×C₇×M₁₆	C₂³	1	4	yes	—
62	C₂×C₇×M₁₆	C₂³	1	4	yes	—
63	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₇×C₈	C₂³	1	2	yes	—
65	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
66	C₇×#126	—	2	16	no	—
67	C₇×#125	—	2	4	no	—
68	C₇×#125	C₂³	1	8	yes	—
69	C₇×#124	—	2	4	no	—
70	C₇×#124	C₂³	1	8	yes	—
71	C₇×#123	—	2	16	no	—
72	C₇×C₂²⋊Q₈	—	2	4	no	—
73	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
74	C₇×#121	—	2	4	no	—
75	C₇×#121	C₂³	1	8	yes	—
76	C₄×C₇×Q₈	—	2	4	no	—
77	C₄×C₇×Q₈	C₂³	1	8	yes	—
78	C₄×C₇×D₄	—	2	16	no	—
79	C₄×C₇×D₄	—	2	4	no	—
80	C₄×C₇×D₄	C₂³	1	8	yes	—
81	C₇×#117	—	2	16	no	—
82	C₂×C₇×C₄⋊C₄	—	2	2	no	—
83	C₂×C₇×C₄⋊C₄	—	2	2	no	—
84	C₂×C₇×C₄⋊C₄	—	2	2	no	—
85	C₂×C₇×C₄⋊C₄	—	2	2	no	—
86	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
87	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
88	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
89	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
90	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
91	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
92	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
93	C₂×C₄²×C₇	—	2	2	no	—
94	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₇	D₄	1	4	yes	—
97	C₂×C₄²×C₇	C₂³	1	2	yes	—
98	C₂×C₄²×C₇	C₂³	1	4	yes	—
99	C₇×#107	C₂³	1	8	yes	—
100	C₇×#106	C₂³	1	4	yes	—
101	C₇×#106	C₂³	1	4	yes	—
102	C₇×C₄⋊C₈	C₂³	1	8	yes	—
103	C₇×C₄⋊C₈	C₂³	1	8	yes	—
104	C₇×#103	C₂³	1	8	yes	—
105	C₇×#103	C₂³	1	8	yes	—
106	C₇×#102	C₂³	1	8	yes	—
107	C₇×#102	C₂³	1	8	yes	—
108	C₂×#529	C₂×C₇	1	2	yes	complemented
109	#3256	C₂×C₇	1	16	yes	direct product factor
110	C₂×#479	C₂×C₇	1	2	yes	complemented
111	C₂×#478	C₂×C₇	1	2	yes	complemented
112	C₂×#470	C₂×C₇	1	1	yes	characteristic, complemented
113	C₂×#469	C₂×C₇	1	1	yes	characteristic
114	C₂×#468	C₂×C₇	1	2	yes	complemented
115	C₂×#464	C₂×C₇	1	2	yes	complemented
116	C₂×#463	C₂×C₇	1	2	yes	complemented
117	C₂×#423	C₂×C₇	1	1	yes	characteristic, complemented
118	C₂⁴×C₇	—	2	2	no	—
119	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
120	C₂×C₇×Q₈	—	2	2	no	—
121	C₂×C₇×Q₈	—	2	4	no	—
122	C₂×C₇×Q₈	—	2	4	no	—
123	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
124	C₂×C₇×D₄	—	2	8	no	—
125	C₂×C₇×D₄	—	2	2	no	—
126	C₂×C₇×D₄	—	2	4	no	—
127	C₂×C₇×D₄	—	2	4	no	—
128	C₂×C₇×D₄	—	4	8	no	—
129	C₂×C₇×D₄	C₂⁴	1	4	yes	—
130	C₂²×C₄×C₇	—	2	2	no	—
131	C₂²×C₄×C₇	—	2	2	no	—
132	C₂²×C₄×C₇	—	2	2	no	—
133	C₂²×C₄×C₇	—	2	2	no	—
134	C₂²×C₄×C₇	—	2	2	no	—
135	C₂²×C₄×C₇	—	2	8	no	—
136	C₂²×C₄×C₇	—	4	4	no	—
137	C₂²×C₄×C₇	—	4	8	no	—
138	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₇	C₂×D₄	1	8	yes	—
143	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
145	C₇×Q₁₆	—	4	4	no	—
146	C₇×SD₁₆	—	4	8	no	—
147	C₇×D₈	—	4	4	no	—
148	C₇×M₁₆	—	4	4	no	—
149	C₇×M₁₆	—	4	4	no	—
150	C₂×C₇×C₈	—	2	2	no	—
151	C₂×C₇×C₈	—	2	4	no	—
152	C₂×C₇×C₈	—	2	2	no	—
153	C₂×C₇×C₈	C₂⁴	1	2	yes	—
154	C₂×C₇×C₈	C₂⁴	1	4	yes	—
155	C₂×C₇×C₈	C₂⁴	1	2	yes	—
156	C₇×C₄⋊C₄	—	2	8	no	—
157	C₇×C₄⋊C₄	—	2	8	no	—
158	C₇×C₄⋊C₄	—	2	8	no	—
159	C₇×C₄⋊C₄	—	2	8	no	—
160	C₇×C₄⋊C₄	—	2	2	no	—
161	C₇×C₄⋊C₄	—	2	2	no	—
162	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
163	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
164	C₇×C₂²⋊C₄	—	2	8	no	—
165	C₇×C₂²⋊C₄	—	2	8	no	—
166	C₇×C₂²⋊C₄	—	2	8	no	—
167	C₇×C₂²⋊C₄	—	2	8	no	—
168	C₇×C₂²⋊C₄	—	2	8	no	—
169	C₄²×C₇	—	2	8	no	—
170	C₄²×C₇	C₂×D₄	1	4	yes	—
171	C₄²×C₇	C₂×D₄	1	4	yes	—
172	C₄²×C₇	C₂×D₄	1	4	yes	—
173	C₄²×C₇	C₂⁴	1	4	yes	—
174	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
175	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
176	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
177	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
178	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
179	#529	—	2	8	no	—
180	#529	C₂²×C₇	1	16	yes	complemented
181	C₂×#126	—	2	2	no	—
182	C₂×#125	C₂²×C₇	1	2	yes	—
183	C₂×#124	C₂²×C₇	1	2	yes	—
184	C₂×#123	—	2	2	no	—
185	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
186	C₂×#121	C₂²×C₇	1	2	yes	—
187	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
188	C₂×C₄×D₄	—	2	2	no	—
189	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
190	C₂×#117	—	2	2	no	—
191	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
192	#479	C₂²×C₇	1	16	yes	complemented
193	#478	C₂²×C₇	1	16	yes	complemented
194	#470	C₂²×C₇	1	8	yes	complemented
195	#469	C₂²×C₇	1	8	yes	—
196	#468	C₂²×C₇	1	16	yes	complemented
197	#464	C₂²×C₇	1	16	yes	complemented
198	#463	C₂²×C₇	1	16	yes	complemented
199	C₂×#107	C₂²×C₇	1	2	yes	—
200	C₂×#106	C₂²×C₇	1	1	yes	characteristic
201	C₂×#106	C₂²×C₇	1	1	yes	characteristic
202	#423	C₂²×C₇	1	8	yes	complemented
203	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
204	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
205	C₂×#103	C₂²×C₇	1	2	yes	—
206	C₂×#103	C₂²×C₇	1	2	yes	—
207	C₂×#102	C₂²×C₇	1	2	yes	—
208	C₂×#102	C₂²×C₇	1	2	yes	—
209	C₂³×C₇	—	2	2	no	—
210	C₂³×C₇	—	2	4	no	—
211	C₂³×C₇	—	2	4	no	—
212	C₂³×C₇	—	4	4	no	—
213	C₂³×C₇	—	4	4	no	—
214	C₂³×C₇	—	4	4	no	—
215	C₂³×C₇	C₂²×D₄	1	2	yes	—
216	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
217	C₇×Q₈	—	2	4	no	—
218	C₇×Q₈	—	2	4	no	—
219	C₇×Q₈	—	4	4	no	—
220	C₇×D₄	—	2	4	no	—
221	C₇×D₄	—	2	4	no	—
222	C₇×D₄	—	4	16	no	—
223	C₇×D₄	—	4	4	no	—
224	C₂×C₄×C₇	—	2	2	no	—
225	C₂×C₄×C₇	—	2	4	no	—
226	C₂×C₄×C₇	—	2	4	no	—
227	C₂×C₄×C₇	—	2	4	no	—
228	C₂×C₄×C₇	—	2	2	no	—
229	C₂×C₄×C₇	—	2	2	no	—
230	C₂×C₄×C₇	—	2	4	no	—
231	C₂×C₄×C₇	—	2	4	no	—
232	C₂×C₄×C₇	—	2	4	no	—
233	C₂×C₄×C₇	—	4	8	no	—
234	C₂×C₄×C₇	—	4	16	no	—
235	C₂×C₄×C₇	—	4	4	no	—
236	C₂×C₄×C₇	—	4	4	no	—
237	C₂×C₄×C₇	—	4	4	no	—
238	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
239	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
240	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
241	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
243	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
244	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
245	C₇×C₈	—	2	2	no	—
246	C₇×C₈	—	2	4	no	—
247	C₇×C₈	—	2	2	no	—
248	C₂²×Q₈	C₂³×C₇	1	2	yes	—
249	C₂²×D₄	—	2	2	no	—
250	C₂²×D₄	C₂³×C₇	1	2	yes	—
251	C₂³×C₄	—	2	2	no	—
252	C₂³×C₄	C₇×D₄	1	2	yes	—
253	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
254	C₂×Q₁₆	—	4	2	no	—
255	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
256	C₂×SD₁₆	—	4	4	no	—
257	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
258	C₂×D₈	—	4	2	no	—
259	C₂×D₈	C₂³×C₇	1	4	yes	—
260	C₂×M₁₆	—	4	2	no	—
261	C₂×M₁₆	—	4	2	no	—
262	C₂×M₁₆	C₂³×C₇	1	4	yes	—
263	C₂×M₁₆	C₂³×C₇	1	4	yes	—
264	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₇	1	2	yes	—
266	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
267	#126	—	2	16	no	—
268	#125	—	2	4	no	—
269	#125	C₂³×C₇	1	8	yes	—
270	#124	—	2	4	no	—
271	#124	C₂³×C₇	1	8	yes	—
272	#123	—	2	16	no	—
273	C₂²⋊Q₈	—	2	4	no	—
274	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
275	#121	—	2	4	no	—
276	#121	C₂³×C₇	1	8	yes	—
277	C₄×Q₈	—	2	4	no	—
278	C₄×Q₈	C₂³×C₇	1	8	yes	—
279	C₄×D₄	—	2	16	no	—
280	C₄×D₄	—	2	4	no	—
281	C₄×D₄	C₂³×C₇	1	8	yes	—
282	#117	—	2	16	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
289	C₂×C₂²⋊C₄	—	2	2	no	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₄²	—	2	2	no	—
295	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
296	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
297	C₂×C₄²	C₇×D₄	1	4	yes	—
298	C₂×C₄²	C₂³×C₇	1	2	yes	—
299	C₂×C₄²	C₂³×C₇	1	4	yes	—
300	#107	C₂³×C₇	1	8	yes	—
301	#106	C₂³×C₇	1	4	yes	—
302	#106	C₂³×C₇	1	4	yes	—
303	C₄⋊C₈	C₂³×C₇	1	8	yes	—
304	C₄⋊C₈	C₂³×C₇	1	8	yes	—
305	#103	C₂³×C₇	1	8	yes	—
306	#103	C₂³×C₇	1	8	yes	—
307	#102	C₂³×C₇	1	8	yes	—
308	#102	C₂³×C₇	1	8	yes	—
309	C₂²×C₇	—	2	2	no	—
310	C₂²×C₇	—	2	4	no	—
311	C₂²×C₇	—	4	4	no	—
312	C₂²×C₇	—	4	4	no	—
313	C₂²×C₇	—	4	4	no	—
314	C₂²×C₇	—	4	4	no	—
315	C₂²×C₇	—	8	8	no	—
316	C₂²×C₇	#537	1	2	yes	—
317	C₂²×C₇	#575	1	4	yes	—
318	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
319	C₄×C₇	—	2	2	no	—
320	C₄×C₇	—	2	4	no	—
321	C₄×C₇	—	2	4	no	—
322	C₄×C₇	—	4	4	no	—
323	C₄×C₇	—	4	4	no	—
324	C₄×C₇	—	4	4	no	—
325	C₄×C₇	#537	1	2	yes	—
326	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
327	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
328	C₂⁴	—	2	2	no	—
329	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	4	no	—
332	C₂×Q₈	—	2	4	no	—
333	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
334	C₂×D₄	—	2	8	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	4	8	no	—
339	C₂×D₄	C₂⁴×C₇	1	4	yes	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	8	no	—
346	C₂²×C₄	—	4	4	no	—
347	C₂²×C₄	—	4	8	no	—
348	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
349	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
350	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
351	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
352	C₂²×C₄	C₂×C₇×D₄	1	8	yes	—
353	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
354	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
355	Q₁₆	—	4	4	no	—
356	SD₁₆	—	4	8	no	—
357	D₈	—	4	4	no	—
358	M₁₆	—	4	4	no	—
359	M₁₆	—	4	4	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	4	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	C₂⁴×C₇	1	2	yes	—
364	C₂×C₈	C₂⁴×C₇	1	4	yes	—
365	C₂×C₈	C₂⁴×C₇	1	2	yes	—
366	C₄⋊C₄	—	2	8	no	—
367	C₄⋊C₄	—	2	8	no	—
368	C₄⋊C₄	—	2	8	no	—
369	C₄⋊C₄	—	2	8	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
373	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
374	C₂²⋊C₄	—	2	8	no	—
375	C₂²⋊C₄	—	2	8	no	—
376	C₂²⋊C₄	—	2	8	no	—
377	C₂²⋊C₄	—	2	8	no	—
378	C₂²⋊C₄	—	2	8	no	—
379	C₄²	—	2	8	no	—
380	C₄²	C₂×C₇×D₄	1	4	yes	—
381	C₄²	C₂×C₇×D₄	1	4	yes	—
382	C₄²	C₂×C₇×D₄	1	4	yes	—
383	C₄²	C₂⁴×C₇	1	4	yes	—
384	C₂×C₇	—	4	2	no	—
385	C₂×C₇	—	8	4	no	—
386	C₂×C₇	#3256	1	4	yes	direct product factor
387	C₂×C₇	C₂×#537	1	1	yes	characteristic
388	C₂×C₇	C₂×#575	1	2	yes	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	4	no	—
391	C₂³	—	2	4	no	—
392	C₂³	—	4	4	no	—
393	C₂³	—	4	4	no	—
394	C₂³	—	4	4	no	—
395	C₂³	C₂²×C₇×D₄	1	2	yes	—
396	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
397	Q₈	—	2	4	no	—
398	Q₈	—	2	4	no	—
399	Q₈	—	4	4	no	—
400	D₄	—	2	4	no	—
401	D₄	—	2	4	no	—
402	D₄	—	4	16	no	—
403	D₄	—	4	4	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	4	8	no	—
414	C₂×C₄	—	4	16	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
419	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
420	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
421	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
422	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
423	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
424	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
425	C₈	—	2	2	no	—
426	C₈	—	2	4	no	—
427	C₈	—	2	2	no	—
428	C₇	C₂×#3256	1	1	yes	characteristic, direct product factor, Sylow
429	C₂²	—	2	4	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	4	4	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	8	8	no	—
436	C₂²	C₇×#537	1	2	yes	—
437	C₂²	C₇×#575	1	4	yes	—
438	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
439	C₄	—	2	4	no	—
440	C₄	—	2	4	no	—
441	C₄	—	2	2	no	—
442	C₄	—	4	4	no	—
443	C₄	—	4	4	no	—
444	C₄	—	4	4	no	—
445	C₄	C₇×#537	1	2	yes	—
446	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
447	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
448	C₂	—	4	2	no	—
449	C₂	—	8	4	no	—
450	C₂	C₇×#3256	1	4	yes	direct product factor
451	C₂	C₂×C₇×#537	1	1	yes	characteristic
452	C₂	C₂×C₇×#575	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂×C₇×#469	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₇×#529	C₂	semidirect
2. C₇×#3256	C₂	direct (N × H)
3. C₂×C₇×#479	C₂	semidirect
4. C₂×C₇×#478	C₂	semidirect
5. C₂×C₇×#470	C₂	semidirect
7. C₂×C₇×#468	C₂	semidirect
8. C₂×C₇×#464	C₂	semidirect
9. C₂×C₇×#463	C₂	semidirect
10. C₂×C₇×#423	C₂	semidirect
17. C₇×#529	C₂²	semidirect
29. C₇×#479	C₂²	semidirect
30. C₇×#478	C₂²	semidirect
31. C₇×#470	C₂²	semidirect
33. C₇×#468	C₂²	semidirect
34. C₇×#464	C₂²	semidirect
35. C₇×#463	C₂²	semidirect
39. C₇×#423	C₂²	semidirect
46. C₂×#3256	C₇	direct (N × H)
108. C₂×#529	C₂×C₇	semidirect
109. #3256	C₂×C₇	direct (N × H)
110. C₂×#479	C₂×C₇	semidirect
111. C₂×#478	C₂×C₇	semidirect
112. C₂×#470	C₂×C₇	semidirect
114. C₂×#468	C₂×C₇	semidirect
115. C₂×#464	C₂×C₇	semidirect
116. C₂×#463	C₂×C₇	semidirect
117. C₂×#423	C₂×C₇	semidirect
180. #529	C₂²×C₇	semidirect
192. #479	C₂²×C₇	semidirect
193. #478	C₂²×C₇	semidirect
194. #470	C₂²×C₇	semidirect
196. #468	C₂²×C₇	semidirect
197. #464	C₂²×C₇	semidirect
198. #463	C₂²×C₇	semidirect
202. #423	C₂²×C₇	semidirect
386. C₂×C₇	#3256	direct (N × H)
428. C₇	C₂×#3256	direct (N × H)
450. C₂	C₇×#3256	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#529	2
C₇×#3256	2
C₂×C₇×#479	2
C₂×C₇×#478	2
C₂×C₇×#470	2
C₂×C₇×#469	2
C₂×C₇×#468	2
C₂×C₇×#464	2
C₂×C₇×#463	2
C₂×C₇×#423	2
C₂×#3256	7

Subgroups — C2×C7×#3256 #13238122

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3256 #13238122